Plots:
Summary plots - For the summary plots, each plot is paired by parameter level vertically and the values in the cells are the mean value across all of the simulations for that parameter level. Sample strategy is on the y-axis and number of sites is on the x-axis.Note that each average encompasses all of the other varying simulation parameters.
Full plots - For the full plots, Each plot represents a unique simulation and the values in the cells are the mean value across all of the 10 iterations of that simulation across all three unique landscape seeds (i.e., all three sets of Neutral Landscape Models) for a total of 30 replicates. Sample strategy is on the y-axis and number of sites is on the x-axis. Since there are a many simulations presented in the full plots, here is a handy key for how the different parameters are laid out within them (H = High, L = Low):
Methods:
K - number of latent factors used in LFMM
TPR - True Positive Rate
FDR - False Discovery Rate
strict vs relaxed TPR/FDR - “relaxed” means any adaptive loci identified was counted as a true positive and “strict” means only an adaptive loci identified with the correct environmental variable was counted as a true positive
pRDA - partial RDA conditioning on two PC axes to control for population genetic structure
lasso vs ridge- “lasso” and “ridge” are different methods utilized by LFMM that have different penalization functions (Caye et al., 2019)
Only results from the ridge method are used from here on out
| Linear mixed effect model | |||||||
| TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0008 | 53.2028 | 53.2028 | 1 | 15.3480K | 1263.83866 | 4.4 × 10−266* |
| Population size | 0.0763 | 22.3781 | 22.3781 | 1 | 15.3480K | 531.59489 | 1.2 × 10−115* |
| Migration | 0.2604 | 260.3385 | 260.3385 | 1 | 15.3480K | 6184.36896 | 0.0* |
| Selection strength | 0.0256 | 2.5157 | 2.5157 | 1 | 15.3480K | 59.76088 | 1.1 × 10−14* |
| Spatial autocorrelation | 0.3835 | 564.7879 | 564.7879 | 1 | 15.3480K | 13416.59552 | 0.0* |
| Environmental correlation | −0.0546 | 11.4612 | 11.4612 | 1 | 15.3480K | 272.26221 | 1.2 × 10−60* |
| * p < 0.001 | |||||||
| Tukey test for TPR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | −0.0009 | 0.0047 | −0.2029 | 0.99704719 | 1.0e+00 |
| ES - R | 0.0114 | 0.0047 | 2.4382 | 0.07008603 | 7.0e-02 |
| ES - T | 0.0513 | 0.0047 | 10.9528 | 3.8 × 10−14 | 3.8e-14 |
| G - R | 0.0124 | 0.0047 | 2.6410 | 0.04118167 | 4.1e-02 |
| G - T | 0.0522 | 0.0047 | 11.1557 | 1.2 × 10−14 | 1.2e-14 |
| R - T | 0.0399 | 0.0047 | 8.5146 | 3.7 × 10−14 | 3.7e-14 |
| Linear mixed effect model | |||||||
| TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0008 | 53.5184 | 53.5184 | 1 | 15.3480K | 1289.21597 | 3.6 × 10−271* |
| Population size | 0.0732 | 20.5782 | 20.5782 | 1 | 15.3480K | 495.71192 | 4.2 × 10−108* |
| Migration | 0.2591 | 257.7774 | 257.7774 | 1 | 15.3480K | 6209.65003 | 0.0* |
| Selection strength | 0.0242 | 2.2525 | 2.2525 | 1 | 15.3480K | 54.26063 | 1.8 × 10−13* |
| Spatial autocorrelation | 0.3761 | 543.2885 | 543.2885 | 1 | 15.3480K | 13087.38352 | 0.0* |
| Environmental correlation | −0.0567 | 12.3237 | 12.3237 | 1 | 15.3480K | 296.86851 | 6.6 × 10−66* |
| * p < 0.001 | |||||||
| Tukey test for TPR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | −0.0020 | 0.0046 | −0.4350 | 0.97243790 | 9.7e-01 |
| ES - R | 0.0108 | 0.0046 | 2.3148 | 0.09463102 | 9.5e-02 |
| ES - T | 0.0522 | 0.0046 | 11.2193 | 8.9 × 10−15 | 8.9e-15 |
| G - R | 0.0128 | 0.0046 | 2.7499 | 0.03037337 | 3.0e-02 |
| G - T | 0.0542 | 0.0046 | 11.6543 | 0.0 | 0.0e+00 |
| R - T | 0.0414 | 0.0046 | 8.9045 | 2.8 × 10−14 | 2.8e-14 |
| Linear mixed effect model | |||||||
| FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0026 | 505.5285 | 505.5285 | 1 | 15.3480K | 4.033406e+03 | 0.0* |
| Population size | 0.0070 | 0.1878 | 0.1878 | 1 | 15.3480K | 1.498216e+00 | 0.22 |
| Migration | −0.0004 | 0.0006 | 0.0006 | 1 | 15.3480K | 4.999228e-03 | 0.94 |
| Selection strength | −0.0199 | 1.5277 | 1.5277 | 1 | 15.3480K | 1.218901e+01 | 4.8 × 10−4* |
| Spatial autocorrelation | 0.0552 | 11.7204 | 11.7204 | 1 | 15.3480K | 9.351249e+01 | 4.7 × 10−22* |
| Environmental correlation | 0.0308 | 3.6511 | 3.6511 | 1 | 15.3480K | 2.913101e+01 | 6.9 × 10−8* |
| * p < 0.001 | |||||||
| Tukey test for FDR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | 0.0168 | 0.0081 | 2.0818 | 0.1590172 | 1.6e-01 |
| ES - R | 0.0130 | 0.0081 | 1.6075 | 0.3742953 | 3.7e-01 |
| ES - T | −0.0272 | 0.0081 | −3.3699 | 4.2 × 10−3 | 4.2e-03 |
| G - R | −0.0038 | 0.0081 | −0.4743 | 0.9647549 | 9.6e-01 |
| G - T | −0.0440 | 0.0081 | −5.4517 | 3.0 × 10−7 | 3.0e-07 |
| R - T | −0.0402 | 0.0081 | −4.9774 | 3.8 × 10−6 | 3.8e-06 |
| Linear mixed effect model | |||||||
| FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0025 | 492.6077 | 492.6077 | 1 | 15.3480K | 3893.485885 | 0.0* |
| Population size | 0.0164 | 1.0308 | 1.0308 | 1 | 15.3480K | 8.147285 | 4.3 × 10−3** |
| Migration | 0.0027 | 0.0270 | 0.0270 | 1 | 15.3480K | 0.213428 | 0.6400 |
| Selection strength | −0.0149 | 0.8485 | 0.8485 | 1 | 15.3480K | 6.706348 | 0.0096** |
| Spatial autocorrelation | 0.0734 | 20.6903 | 20.6903 | 1 | 15.3480K | 163.532211 | 3.0 × 10−37* |
| Environmental correlation | 0.0363 | 5.0474 | 5.0474 | 1 | 15.3480K | 39.893688 | 2.8 × 10−10* |
| * p < 0.001 | |||||||
| ** p < 0.01 | |||||||
| Tukey test for FDR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | 0.0191 | 0.0081 | 2.3496 | 0.08711056 | 8.7e-02 |
| ES - R | 0.0144 | 0.0081 | 1.7719 | 0.28690133 | 2.9e-01 |
| ES - T | −0.0285 | 0.0081 | −3.5108 | 2.5 × 10−3 | 2.5e-03 |
| G - R | −0.0047 | 0.0081 | −0.5776 | 0.93881608 | 9.4e-01 |
| G - T | −0.0476 | 0.0081 | −5.8604 | 2.8 × 10−8 | 2.8e-08 |
| R - T | −0.0429 | 0.0081 | −5.2827 | 7.6 × 10−7 | 7.6e-07 |
Only results from the ridge method are used from here on out
| Linear mixed effect model | |||||||
| TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0029 | 3.2042 | 3.2042 | 1 | 8.6290K | 140.5760485 | 3.5 × 10−32* |
| Population size | 0.0308 | 2.0477 | 2.0477 | 1 | 8.6290K | 89.8352521 | 3.3 × 10−21* |
| Migration | 0.0787 | 13.3647 | 13.3647 | 1 | 8.6290K | 586.3375067 | 2.2 × 10−125* |
| Selection strength | −0.0015 | 0.0047 | 0.0047 | 1 | 8.6290K | 0.2052864 | 0.65 |
| Spatial autocorrelation | 0.1968 | 83.6960 | 83.6960 | 1 | 8.6290K | 3671.9104037 | 0.0* |
| Environmental correlation | −0.0566 | 6.9313 | 6.9313 | 1 | 8.6290K | 304.0919069 | 5.9 × 10−67* |
| * p < 0.001 | |||||||
| Tukey test for TPR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0269 | 0.0040 | −6.7676 | 3.9 × 10−11 | 3.9e-11 |
| EQ - R | −0.0074 | 0.0040 | −1.8703 | 0.147366 | 1.5e-01 |
| ES - R | 0.0195 | 0.0040 | 4.8974 | 2.9 × 10−6 | 2.9e-06 |
| Linear mixed effect model | |||||||
| TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0020 | 1.4302 | 1.4302 | 1 | 8.6290K | 67.970410 | 1.9 × 10−16* |
| Population size | 0.0284 | 1.7480 | 1.7480 | 1 | 8.6290K | 83.077065 | 9.7 × 10−20* |
| Migration | 0.0868 | 16.2650 | 16.2650 | 1 | 8.6290K | 773.013161 | 5.2 × 10−163* |
| Selection strength | −0.0034 | 0.0245 | 0.0245 | 1 | 8.6290K | 1.163182 | 0.28 |
| Spatial autocorrelation | 0.1897 | 77.7389 | 77.7389 | 1 | 8.6290K | 3694.635667 | 0.0* |
| Environmental correlation | −0.0562 | 6.8328 | 6.8328 | 1 | 8.6290K | 324.738752 | 2.7 × 10−71* |
| * p < 0.001 | |||||||
| Tukey test for TPR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0234 | 0.0038 | −6.1133 | 2.9 × 10−9 | 2.9e-09 |
| EQ - R | −0.0046 | 0.0038 | −1.1935 | 0.4570187 | 4.6e-01 |
| ES - R | 0.0188 | 0.0038 | 4.9198 | 2.6 × 10−6 | 2.6e-06 |
| Linear mixed effect model | |||||||
| FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0178 | 117.4584 | 117.4584 | 1 | 8.6290K | 2365.005677 | 0.0* |
| Population size | 0.0054 | 0.0639 | 0.0639 | 1 | 8.6290K | 1.285793 | 0.26 |
| Migration | −0.0658 | 9.3587 | 9.3587 | 1 | 8.6290K | 188.434971 | 1.9 × 10−42* |
| Selection strength | −0.0066 | 0.0953 | 0.0953 | 1 | 8.6290K | 1.918980 | 0.17 |
| Spatial autocorrelation | −0.0233 | 1.1748 | 1.1748 | 1 | 8.6290K | 23.654165 | 1.2 × 10−6* |
| Environmental correlation | 0.0062 | 0.0820 | 0.0820 | 1 | 8.6290K | 1.651659 | 0.20 |
| * p < 0.001 | |||||||
| Tukey test for FDR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0424 | 0.0059 | −7.2249 | 1.5 × 10−12 | 1.5e-12 |
| EQ - R | −0.0509 | 0.0059 | −8.6624 | 2.5 × 10−14 | 2.5e-14 |
| ES - R | −0.0084 | 0.0059 | −1.4376 | 0.3215746 | 3.2e-01 |
| Linear mixed effect model | |||||||
| FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | −0.0177 | 115.9461 | 115.9461 | 1 | 8.6290K | 2333.109893 | 0.0* |
| Population size | 0.0063 | 0.0856 | 0.0856 | 1 | 8.6290K | 1.723408 | 0.19 |
| Migration | −0.0650 | 9.1374 | 9.1374 | 1 | 8.6290K | 183.866796 | 1.8 × 10−41* |
| Selection strength | −0.0065 | 0.0927 | 0.0927 | 1 | 8.6290K | 1.864595 | 0.17 |
| Spatial autocorrelation | −0.0205 | 0.9050 | 0.9050 | 1 | 8.6290K | 18.210895 | 2.0 × 10−5* |
| Environmental correlation | 0.0069 | 0.1024 | 0.1024 | 1 | 8.6290K | 2.061300 | 0.15 |
| * p < 0.001 | |||||||
| Tukey test for FDR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0433 | 0.0059 | −7.3719 | 5.2 × 10−13 | 5.2e-13 |
| EQ - R | −0.0507 | 0.0059 | −8.6318 | 2.6 × 10−14 | 2.6e-14 |
| ES - R | −0.0074 | 0.0059 | −1.2599 | 0.4179973 | 4.2e-01 |
Only results from the standard RDA (not the partial RDA) are used from here on out
| Linear mixed effect model | |||||||
| TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0007 | 37.4207 | 37.4207 | 1 | 15.3480K | 860.515512 | 4.3 × 10−184* |
| Population size | 0.0374 | 5.3737 | 5.3737 | 1 | 15.3480K | 123.571864 | 1.3 × 10−28* |
| Migration | 0.2896 | 321.9753 | 321.9753 | 1 | 15.3480K | 7404.049535 | 0.0* |
| Selection strength | −0.0037 | 0.0516 | 0.0516 | 1 | 15.3480K | 1.185546 | 0.28 |
| Spatial autocorrelation | 0.2868 | 315.8296 | 315.8296 | 1 | 15.3480K | 7262.724755 | 0.0* |
| Environmental correlation | 0.0169 | 1.0931 | 1.0931 | 1 | 15.3480K | 25.136567 | 5.4 × 10−7* |
| * p < 0.001 | |||||||
| Tukey test for TPR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | −0.0004 | 0.0048 | −0.0747 | 0.9998509 | 1.0e+00 |
| ES - R | 0.0089 | 0.0048 | 1.8779 | 0.2375584 | 2.4e-01 |
| ES - T | 0.0333 | 0.0048 | 6.9911 | 1.6 × 10−11 | 1.6e-11 |
| G - R | 0.0093 | 0.0048 | 1.9525 | 0.2062836 | 2.1e-01 |
| G - T | 0.0336 | 0.0048 | 7.0658 | 9.6 × 10−12 | 9.6e-12 |
| R - T | 0.0243 | 0.0048 | 5.1133 | 1.9 × 10−6 | 1.9e-06 |
| Linear mixed effect model | |||||||
| TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0006 | 32.6703 | 32.6703 | 1 | 15.3480K | 841.258694 | 4.0 × 10−180* |
| Population size | 0.0340 | 4.4409 | 4.4409 | 1 | 15.3480K | 114.352267 | 1.4 × 10−26* |
| Migration | 0.2673 | 274.3571 | 274.3571 | 1 | 15.3480K | 7064.686800 | 0.0* |
| Selection strength | −0.0054 | 0.1111 | 0.1111 | 1 | 15.3480K | 2.859800 | 0.091 |
| Spatial autocorrelation | 0.2643 | 268.3236 | 268.3236 | 1 | 15.3480K | 6909.325831 | 0.0* |
| Environmental correlation | 0.0036 | 0.0495 | 0.0495 | 1 | 15.3480K | 1.274395 | 0.260 |
| * p < 0.001 | |||||||
| Tukey test for TPR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | 0.0000 | 0.0045 | −0.0090 | 0.9999997 | 1.0e+00 |
| ES - R | 0.0087 | 0.0045 | 1.9315 | 0.2147867 | 2.1e-01 |
| ES - T | 0.0342 | 0.0045 | 7.6014 | 2.0 × 10−13 | 2.0e-13 |
| G - R | 0.0087 | 0.0045 | 1.9405 | 0.2111304 | 2.1e-01 |
| G - T | 0.0342 | 0.0045 | 7.6104 | 1.9 × 10−13 | 1.9e-13 |
| R - T | 0.0255 | 0.0045 | 5.6699 | 8.6 × 10−8 | 8.6e-08 |
| Linear mixed effect model | |||||||
| FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0002 | 3.7712 | 3.7712 | 1 | 15.3480K | 80.61223 | 3.1 × 10−19* |
| Population size | 0.0151 | 0.8807 | 0.8807 | 1 | 15.3480K | 18.82572 | 1.4 × 10−5* |
| Migration | 0.1369 | 71.9514 | 71.9514 | 1 | 15.3480K | 1538.02432 | 1.1 × 10−320* |
| Selection strength | −0.0121 | 0.5603 | 0.5603 | 1 | 15.3480K | 11.97778 | 5.4 × 10−4* |
| Spatial autocorrelation | −0.0490 | 9.2366 | 9.2366 | 1 | 15.3480K | 197.43966 | 1.4 × 10−44* |
| Environmental correlation | 0.0221 | 1.8688 | 1.8688 | 1 | 15.3480K | 39.94790 | 2.7 × 10−10* |
| * p < 0.001 | |||||||
| Tukey test for FDR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | −0.0092 | 0.0049 | −1.8701 | 0.2409603 | 0.24000 |
| ES - R | 0.0063 | 0.0049 | 1.2790 | 0.5763683 | 0.58000 |
| ES - T | 0.0094 | 0.0049 | 1.9034 | 0.2265099 | 0.23000 |
| G - R | 0.0155 | 0.0049 | 3.1491 | 8.9 × 10−3 | 0.00890 |
| G - T | 0.0186 | 0.0049 | 3.7736 | 9.3 × 10−4 | 0.00093 |
| R - T | 0.0031 | 0.0049 | 0.6245 | 0.9242557 | 0.92000 |
| Linear mixed effect model | |||||||
| FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0003 | 4.9052 | 4.9052 | 1 | 15.3480K | 96.998095 | 8.1 × 10−23* |
| Population size | 0.0208 | 1.6581 | 1.6581 | 1 | 15.3480K | 32.788661 | 1.0 × 10−8* |
| Migration | 0.1636 | 102.8145 | 102.8145 | 1 | 15.3480K | 2033.124890 | 0.0* |
| Selection strength | −0.0083 | 0.2627 | 0.2627 | 1 | 15.3480K | 5.194032 | 0.023** |
| Spatial autocorrelation | −0.0199 | 1.5265 | 1.5265 | 1 | 15.3480K | 30.186505 | 4.0 × 10−8* |
| Environmental correlation | 0.0400 | 6.1469 | 6.1469 | 1 | 15.3480K | 121.553432 | 3.7 × 10−28* |
| * p < 0.001 | |||||||
| ** p < 0.05 | |||||||
| Tukey test for FDR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| ES - G | −0.0085 | 0.0051 | −1.6486 | 0.3513345 | 0.3500 |
| ES - R | 0.0080 | 0.0051 | 1.5562 | 0.4039088 | 0.4000 |
| ES - T | 0.0089 | 0.0051 | 1.7350 | 0.3054615 | 0.3100 |
| G - R | 0.0164 | 0.0051 | 3.2048 | 7.4 × 10−3 | 0.0074 |
| G - T | 0.0174 | 0.0051 | 3.3835 | 4.0 × 10−3 | 0.0040 |
| R - T | 0.0009 | 0.0051 | 0.1787 | 0.9979738 | 1.0000 |
Only results from the standard RDA (not the partial RDA) are used from here on out
| Linear mixed effect model | |||||||
| TPR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0032 | 3.7382 | 3.7382 | 1 | 8.6290K | 126.204793 | 4.4 × 10−29* |
| Population size | −0.0256 | 1.4139 | 1.4139 | 1 | 8.6290K | 47.732732 | 5.2 × 10−12* |
| Migration | 0.3026 | 197.8044 | 197.8044 | 1 | 8.6290K | 6677.977925 | 0.0* |
| Selection strength | 0.0247 | 1.3192 | 1.3192 | 1 | 8.6290K | 44.536716 | 2.7 × 10−11* |
| Spatial autocorrelation | 0.2649 | 151.5702 | 151.5702 | 1 | 8.6290K | 5117.088582 | 0.0* |
| Environmental correlation | −0.0095 | 0.1964 | 0.1964 | 1 | 8.6290K | 6.630773 | 0.01 |
| * p < 0.001 | |||||||
| Tukey test for TPR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0076 | 0.0045 | −1.6762 | 0.2143549 | 2.1e-01 |
| EQ - R | 0.0216 | 0.0045 | 4.7556 | 5.9 × 10−6 | 5.9e-06 |
| ES - R | 0.0292 | 0.0045 | 6.4317 | 3.8 × 10−10 | 3.8e-10 |
| Linear mixed effect model | |||||||
| TPR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0035 | 4.5757 | 4.5757 | 1 | 8.6290K | 179.59833 | 1.5 × 10−40* |
| Population size | −0.0218 | 1.0312 | 1.0312 | 1 | 8.6290K | 40.47586 | 2.1 × 10−10* |
| Migration | 0.2649 | 151.6270 | 151.6270 | 1 | 8.6290K | 5951.39931 | 0.0* |
| Selection strength | 0.0171 | 0.6304 | 0.6304 | 1 | 8.6290K | 24.74158 | 6.7 × 10−7* |
| Spatial autocorrelation | 0.2326 | 116.8869 | 116.8869 | 1 | 8.6290K | 4587.84166 | 0.0* |
| Environmental correlation | −0.0218 | 1.0254 | 1.0254 | 1 | 8.6290K | 40.24545 | 2.4 × 10−10* |
| * p < 0.001 | |||||||
| Tukey test for TPR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | −0.0071 | 0.0042 | −1.6889 | 0.2094071 | 2.1e-01 |
| EQ - R | 0.0183 | 0.0042 | 4.3478 | 4.1 × 10−5 | 4.1e-05 |
| ES - R | 0.0254 | 0.0042 | 6.0367 | 4.7 × 10−9 | 4.7e-09 |
| Linear mixed effect model | |||||||
| FDR relaxed ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0031 | 3.6639 | 3.6639 | 1 | 8.6290K | 56.113654 | 7.5 × 10−14* |
| Population size | −0.3353 | 242.8022 | 242.8022 | 1 | 8.6290K | 3718.564269 | 0.0* |
| Migration | 0.6147 | 816.1570 | 816.1570 | 1 | 8.6290K | 12499.609497 | 0.0* |
| Selection strength | 0.0220 | 1.0484 | 1.0484 | 1 | 8.6290K | 16.056600 | 6.2 × 10−5* |
| Spatial autocorrelation | −0.0630 | 8.5651 | 8.5651 | 1 | 8.6290K | 131.176414 | 3.7 × 10−30* |
| Environmental correlation | 0.0143 | 0.4433 | 0.4433 | 1 | 8.6290K | 6.788829 | 0.0092** |
| * p < 0.001 | |||||||
| ** p < 0.01 | |||||||
| Tukey test for FDR relaxed | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | 0.0026 | 0.0067 | 0.3862 | 0.9210664 | 0.92 |
| EQ - R | 0.0100 | 0.0067 | 1.4820 | 0.2995710 | 0.30 |
| ES - R | 0.0074 | 0.0067 | 1.0957 | 0.5166979 | 0.52 |
| Linear mixed effect model | |||||||
| FDR strict ~ sample number + sampling strategy + population size + migration + selection strength + spatial autocorrelation + environmental correlation + (1 | seed) | |||||||
| Predictors | Fixed Effects | Sum Sq | Mean Sq | NumDF | DenDF | F value | Pr(>F) |
|---|---|---|---|---|---|---|---|
| Sample number | 0.0028 | 2.8102 | 2.8102 | 1 | 8.6290K | 44.31433 | 3.0 × 10−11* |
| Population size | −0.3134 | 212.1999 | 212.1999 | 1 | 8.6290K | 3346.14362 | 0.0* |
| Migration | 0.6419 | 890.0377 | 890.0377 | 1 | 8.6290K | 14034.85129 | 0.0* |
| Selection strength | 0.0267 | 1.5441 | 1.5441 | 1 | 8.6290K | 24.34830 | 8.2 × 10−7* |
| Spatial autocorrelation | −0.0410 | 3.6335 | 3.6335 | 1 | 8.6290K | 57.29578 | 4.1 × 10−14* |
| Environmental correlation | 0.0233 | 1.1743 | 1.1743 | 1 | 8.6290K | 18.51783 | 1.7 × 10−5* |
| * p < 0.001 | |||||||
| Tukey test for FDR strict | |||||
| pairwise ~ sampstrat | |||||
| Contrast | Estimate | SE | Z ratio | p | p |
|---|---|---|---|---|---|
| EQ - ES | 0.0020 | 0.0066 | 0.3010 | 0.9512842 | 0.95 |
| EQ - R | 0.0120 | 0.0066 | 1.8016 | 0.1690281 | 0.17 |
| ES - R | 0.0100 | 0.0066 | 1.5006 | 0.2906260 | 0.29 |
# When migration and autocorrelation were both high (and other parameters are held constant), the strict true positive rate for LFMM was XXX for the E-space sampling scheme versus YYY for transect sampling with a sample size of 225 individuals
lfmm_ind %>%
filter(K == 2, phi == 1, m == 1, H == 0.5, r == 0.3) %>%
group_by(nsamp, sampstrat) %>%
summarise(mean(TPRCOMBO_strict)) %>%
filter(nsamp == 225, sampstrat == "ES" | sampstrat == "T")
## # A tibble: 2 × 3
## # Groups: nsamp [1]
## nsamp sampstrat `mean(TPRCOMBO_strict)`
## <fct> <fct> <dbl>
## 1 225 ES 0.911
## 2 225 T 0.806
# Reduction in performance with transect sampling
df %>%
ungroup() %>%
filter(K == 2, phi == 1, m == 1, H == 0.5, r == 0.3) %>%
filter(sampling == "individual") %>%
select(K, phi, m, seed, H, r, it, TPRCOMBO_strict, sampstrat, Method, nsamp) %>%
pivot_wider(names_from = sampstrat, values_from = TPRCOMBO_strict) %>%
group_by(K, phi, m, seed, H, r, it, nsamp, Method) %>%
mutate(T_dif = mean(c(T - ES, T - G, T - R))) %>%
group_by(Method) %>%
summarize(mean = round(mean(T_dif),3), sd = round(sd(T_dif),3))
## # A tibble: 2 × 3
## Method mean sd
## <chr> <dbl> <dbl>
## 1 LFMM -0.084 0.19
## 2 RDA -0.092 0.151
# Reduction in TPR for strict vs relaxed
# Across methods:
df %>%
ungroup() %>%
filter(sampling == "individual") %>%
mutate(dif = TPRCOMBO_relaxed - TPRCOMBO_strict) %>%
group_by(Method) %>%
summarize(mean = round(mean(dif),3), sd = round(sd(dif),3))
## # A tibble: 2 × 3
## Method mean sd
## <chr> <dbl> <dbl>
## 1 LFMM 0.004 0.027
## 2 RDA 0.011 0.055
# Across methods + r:
df %>%
ungroup() %>%
filter(sampling == "individual") %>%
mutate(dif = TPRCOMBO_relaxed - TPRCOMBO_strict) %>%
group_by(Method, r) %>%
summarize(mean = round(mean(dif),3), sd = round(sd(dif),3))
## # A tibble: 4 × 4
## # Groups: Method [2]
## Method r mean sd
## <chr> <fct> <dbl> <dbl>
## 1 LFMM 0.3 0.003 0.022
## 2 LFMM 0.6 0.005 0.03
## 3 RDA 0.3 0.005 0.036
## 4 RDA 0.6 0.018 0.068
# Average TPR at 255 samples:
df %>%
ungroup() %>%
filter(K == 2, phi == 1, m == 1, H == 0.5, r == 0.3) %>%
filter(nsamp == 225 | nsamp == 25) %>%
group_by(Method, sampling) %>%
summarise(mean = mean(TPRCOMBO_strict, na.rm = TRUE))
## # A tibble: 4 × 3
## # Groups: Method [2]
## Method sampling mean
## <chr> <chr> <dbl>
## 1 LFMM individual 0.893
## 2 LFMM site 0.433
## 3 RDA individual 0.694
## 4 RDA site 0.591
# TPR and FDR for E-Space site-based sampling
df %>%
ungroup() %>%
filter(K == 2, phi == 1, m == 1, H == 0.5, r == 0.3) %>%
filter(sampling == "site", Method == "RDA") %>%
group_by(Method, sampstrat, nsamp) %>%
summarise(TPR = mean(TPRCOMBO_strict, na.rm = TRUE), FDR = mean(FDRCOMBO_strict, na.rm = TRUE)) %>%
arrange(nsamp)
## # A tibble: 9 × 5
## # Groups: Method, sampstrat [3]
## Method sampstrat nsamp TPR FDR
## <chr> <fct> <fct> <dbl> <dbl>
## 1 RDA ES 9 0.452 0.241
## 2 RDA R 9 0.337 0.264
## 3 RDA EQ 9 0.358 0.285
## 4 RDA ES 16 0.564 0.257
## 5 RDA R 16 0.508 0.243
## 6 RDA EQ 16 0.600 0.292
## 7 RDA ES 25 0.621 0.341
## 8 RDA R 25 0.552 0.281
## 9 RDA EQ 25 0.599 0.323